If a, b, c are distinct, then the value of x satisfying $\begin{vmatrix}0&x^2-a&x^3-b\\x^2+a&0&x^2+c\\x^2+b&x-c&0\end{vmatrix}=0$, is

0

For x = 0, we observe that the LHS of the given equation reduces to the determinant of a skew-symmetric matrix of odd order which is always zero. Hence, x = 0 is a solution of the given equation.